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C3×AGL(1,𝔽43) #19129353

order5418
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×AGL(1,𝔽43)
unambiguous semidirect product(D43⋊C3)⋊(C3×C7)
unambiguous semidirect product(D43⋊C7)⋊C32
unambiguous semidirect product(C3×D43⋊C3)⋊C7
unambiguous semidirect product((C43⋊C3)⋊C7)⋊(C2×C3)
unambiguous semidirect product(C3×D43⋊C7)⋊C3

Splittings

Fitting, socleC3×C43 ⋊ C2×C3×C7
derived, SylowC43 ⋊ C2×C32×C7
HallC3×(C43⋊C3)⋊C7 ⋊ C2
HallC3×D43⋊C3 ⋊ C7
HallD43⋊C7 ⋊ C32
HallC3×C43⋊C3 ⋊ C2×C7
HallC43⋊C7 ⋊ C2×C32
HallD43 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC3AGL(1,𝔽43)
commutator, hypocenterC43C2×C32×C7
FrattiniC1G
Fitting, socleC3×C43C2×C3×C7
LCSG ▷ C43
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽43), C2×C3×AGL(1,𝔽43), C3×C5×AGL(1,𝔽43), …
maximal normal subgroup ofD3×AGL(1,𝔽43), C2×C3×AGL(1,𝔽43), C3×C5×AGL(1,𝔽43), …
maximal quotient ofC3×((C43⋊C3)⋊C4)⋊C7, C2×C3×AGL(1,𝔽43), C3×C5×AGL(1,𝔽43), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5418, 32);